28,644 research outputs found
Deriving N-soliton solutions via constrained flows
The soliton equations can be factorized by two commuting x- and t-constrained
flows. We propose a method to derive N-soliton solutions of soliton equations
directly from the x- and t-constrained flows.Comment: 8 pages, AmsTex, no figures, to be published in Journal of Physics
Constructing N-soliton solution for the mKdV equation through constrained flows
Based on the factorization of soliton equations into two commuting integrable
x- and t-constrained flows, we derive N-soliton solutions for mKdV equation via
its x- and t-constrained flows. It shows that soliton solution for soliton
equations can be constructed directly from the constrained flows.Comment: 10 pages, Latex, to be published in "J. Phys. A: Math. Gen.
Negaton and Positon solutions of the soliton equation with self-consistent sources
The KdV equation with self-consistent sources (KdVES) is used as a model to
illustrate the method. A generalized binary Darboux transformation (GBDT) with
an arbitrary time-dependent function for the KdVES as well as the formula for
-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund
transformation between two KdV equations with different degrees of sources and
enable us to construct more general solutions with arbitrary -dependent
functions. By taking the special -function, we obtain multisoliton,
multipositon, multinegaton, multisoliton-positon, multinegaton-positon and
multisoliton-negaton solutions of KdVES. Some properties of these solutions are
discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge
Oxygen-vacancy-mediated Negative Differential Resistance in La and Mg co-substituted BiFeO3 Thin Film
The conductive characteristics of Bi0.9La0.1Fe0.96Mg0.04O3(BLFM) thin film
are investigated at various temperatures and a negative differential resistance
(NDR) is observed in the thin film, where a leakage current peak occurs upon
application of a downward electric field above 80 oC. The origin of the NDR
behavior is shown to be related to the ionic defect of oxygen vacancies (VO..)
present in the film. On the basis of analyzing the leakage mechanism and
surface potential behavior, the NDR behavior can be understood by considering
the competition between the polarized distribution and neutralization of VO..
Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force
We propose a high-resolution microscopy technique for enantiospecific detection of chiral samples down to sub-100-nm size based on force measurement. We delve into the differential photoinduced optical force ΔF exerted on an achiral probe in the vicinity of a chiral sample when left and right circularly polarized beams separately excite the sample-probe interactive system. We analytically prove that ΔF is entangled with the enantiomer type of the sample enabling enantiospecific detection of chiral inclusions. Moreover, we demonstrate that ΔF is linearly dependent on both the chiral response of the sample and the electric response of the tip and is inversely related to the quartic power of probe-sample distance. We provide physical insight into the transfer of optical activity from the chiral sample to the achiral tip based on a rigorous analytical approach. We support our theoretical achievements by several numerical examples highlighting the potential application of the derived analytic properties. Lastly, we demonstrate the sensitivity of our method to enantiospecify nanoscale chiral samples with chirality parameter on the order of 0.01 and discuss how the sensitivity of our proposed technique can be further improved
Higher Order Potential Expansion for the Continuous Limits of the Toda Hierarchy
A method for introducing the higher order terms in the potential expansion to
study the continuous limits of the Toda hierarchy is proposed in this paper.
The method ensures that the higher order terms are differential polynomials of
the lower ones and can be continued to be performed indefinitly. By introducing
the higher order terms, the fewer equations in the Toda hierarchy are needed in
the so-called recombination method to recover the KdV hierarchy. It is shown
that the Lax pairs, the Poisson tensors, and the Hamiltonians of the Toda
hierarchy tend towards the corresponding ones of the KdV hierarchy in
continuous limit.Comment: 20 pages, Latex, to be published in Journal of Physics
The Solutions of the NLS Equations with Self-Consistent Sources
We construct the generalized Darboux transformation with arbitrary functions
in time for the AKNS equation with self-consistent sources (AKNSESCS)
which, in contrast with the Darboux transformation for the AKNS equation,
provides a non-auto-B\"{a}cklund transformation between two AKNSESCSs with
different degrees of sources. The formula for N-times repeated generalized
Darboux transformation is proposed. By reduction the generalized Darboux
transformation with arbitrary functions in time for the Nonlinear
Schr\"{o}dinger equation with self-consistent sources (NLSESCS) is obtained and
enables us to find the dark soliton, bright soliton and positon solutions for
NLSESCS and NLSESCS. The properties of these solution are analyzed.Comment: 24 pages, 3 figures, to appear in Journal of Physics A: Mathematical
and Genera
On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability
The Particle-In-Cell (PIC) method is widely used in relativistic particle
beam and laser plasma modeling. However, the PIC method exhibits numerical
instabilities that can render unphysical simulation results or even destroy the
simulation. For electromagnetic relativistic beam and plasma modeling, the most
relevant numerical instabilities are the finite grid instability and the
numerical Cherenkov instability. We review the numerical dispersion relation of
the electromagnetic PIC algorithm to analyze the origin of these instabilities.
We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm,
and then specialize to the Yee FDTD scheme. In particular, we account for the
manner in which the PIC algorithm updates and samples the fields and
distribution function. Temporal and spatial phase factors from solving
Maxwell's equations on the Yee grid with the leapfrog scheme are also
explicitly accounted for. Numerical solutions to the electrostatic-like modes
in the 1D dispersion relation for a cold drifting plasma are obtained for
parameters of interest. In the succeeding analysis, we investigate how the
finite grid instability arises from the interaction of the numerical 1D modes
admitted in the system and their aliases. The most significant interaction is
due critically to the correct represenation of the operators in the dispersion
relation. We obtain a simple analytic expression for the peak growth rate due
to this interaction.Comment: 25 pages, 6 figure
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